code: def _de_casteljau1(beta, t):
      next_beta = beta[:-1] * (1 - t) + beta[1:] * t
      return next_beta
  
imports: from functools import lru_cache
  import math
  import warnings
  import numpy
  from matplotlib import _api
label_desc: Use image node_id 4 for calling a global function with example usage: _de_casteljau1(beta, t) and returns: next_beta